Find two solutions for each of following equations : (i) 4 x+3 y=12 (ii) 2 x+5 y=0 (iii) 3 y+4=0

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4. Linear Equations in Two Variables

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Find two solutions for each of the following equations :

$(i)$ $4 x+3 y=12$

$(ii)$ $2 x+5 y=0$

$(iii)$ $3 y+4=0$

Option A

Option B

Option C

Option D

Solution

$ (i)$ Taking $x=0,$ we get $3 y=12,$ i.e., $y=4 .$ So, $(0,\,4)$ is a solution of the given equation. Similarly, by taking $y=0,$ we get $x=3 .$ Thus, $(3,\,0) $ is also a solution.

$(ii)$ Taking $x=0,$ we get $5 y=0,$ i.e., $y=0 .$ So $(0,\,0)$ is a solution of the given equation.

Now, if you take $y=0,$ you again get $(0,\,0)$ as a solution, which is the same as the earlier one. To get another solution, take $x=1,$ say. Then you can check that the corresponding value of $y$ is $-\frac{2}{5} \cdot$ So $\left(1,-\frac{2}{5}\right)$ is another solution of $2 x+5 y=0$

$(iii)$ Writing the equation $3 y+4=0$ as $0 . x+3 y+4=0,$ you will find that $y=-\frac{4}{3}$ for any value of $x$. Thus, two solutions can be given as $\left(0,-\frac{4}{3}\right)$ and $\left(1,-\frac{4}{3}\right)$.

Standard 9

Mathematics

From the choices given below, choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$.

For Fig. $(i)$ For Fig. $(ii)$

$(a)$ $y=x$ $(a)$ $y=x+2$

$(b)$ $x+y=0$ $(b)$ $y=x-2$

$(c)$ $y=2 x$ $(c)$ $y=-x+2$

$(d)$ $2+3 y=7 x$ $(d)$ $x+2 y=6$

easy

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be $\rm {Rs.}$ $x$ and that of a pen to be $\rm {Rs.}$ $y$).

easy

Check the solutions of the equation $x -2y = 4$ and which are not : $(4,\,0)$

easy

Draw the graph and linear equations in two variables : $3 = 2x + y$

medium

The taxi fare in a city is as follows :

For the first kilometre, the fare is Rs. $8$ and for the subsequent distance it is Rs. $5$ per $km$. Taking the distance covered as $x\, km$ and total fare as Rs. $y$, write a linear equation for this information, and draw its graph.

medium

Find two solutions for each of the following equations : $(i)$ $4 x+3 y=12$ $(ii)$ $2 x+5 y=0$ $(iii)$ $3 y+4=0$

Solution

Similar Questions

From the choices given below, choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$. For Fig. $(i)$ For Fig. $(ii)$ $(a)$ $y=x$ $(a)$ $y=x+2$ $(b)$ $x+y=0$ $(b)$ $y=x-2$ $(c)$ $y=2 x$ $(c)$ $y=-x+2$ $(d)$ $2+3 y=7 x$ $(d)$ $x+2 y=6$

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be $\rm {Rs.}$ $x$ and that of a pen to be $\rm {Rs.}$ $y$).

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Draw the graph and linear equations in two variables : $3 = 2x + y$

The taxi fare in a city is as follows : For the first kilometre, the fare is Rs. $8$ and for the subsequent distance it is Rs. $5$ per $km$. Taking the distance covered as $x\, km$ and total fare as Rs. $y$, write a linear equation for this information, and draw its graph.

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Find two solutions for each of the following equations :

$(i)$ $4 x+3 y=12$

$(ii)$ $2 x+5 y=0$

$(iii)$ $3 y+4=0$

From the choices given below, choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$.

For Fig. $(i)$ For Fig. $(ii)$

$(a)$ $y=x$ $(a)$ $y=x+2$

$(b)$ $x+y=0$ $(b)$ $y=x-2$

$(c)$ $y=2 x$ $(c)$ $y=-x+2$

$(d)$ $2+3 y=7 x$ $(d)$ $x+2 y=6$

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be $\rm {Rs.}$ $x$ and that of a pen to be $\rm {Rs.}$ $y$).

The taxi fare in a city is as follows :

For the first kilometre, the fare is Rs. $8$ and for the subsequent distance it is Rs. $5$ per $km$. Taking the distance covered as $x\, km$ and total fare as Rs. $y$, write a linear equation for this information, and draw its graph.